Moreover, the headings (h1 thru h6) usually use the same font
as the ordinary paragraphs (p), or at least it is advisable
to do so. In that case the font-family need not be mentioned
with the headers (h1 thru h6), but it can be under body.

Here is another example - this time created by Microsoft
Outlook Express 6. So it's an e-mail. They did use CSS here,
but inline, intermingled with the text, and repeated again
and again in every single paragraph, or even in smaller
pieces of text, even where the representation is identical.
This is not the way to do it!